(■ '74 J 
Dt. Wallis in his Opus Aritbmeticum publiflied A. C. 1 65-7; 
Cap. 33. Prop . 68. reduced the Fraction ~- K by perpetual 
Divifion into the Series A -f AR -f- AR z -\- AR 3 -\~ AR+’t &c. 
Vifcount Brcunker fquared the Hyperbola by this Series 
-- — | — 5 — | — & c - that IS by this, 1 — £-£■£—£■ 
Ar r — 7 -f 7 -bee- conjoyning every two Terms into 
one. And the Quadrature was publiflied in the Pbilofopbical 
Tranjattions tot April 1668. 
Mr. Mercator loon after publiflied a Demonftration of 
this Quadrature by the Divifion of Dr. Wallis ; and foon af- 
ter that Mr. James Gregory publiflied a Geometrical Demon- 
ftration thereof. And thefe Books were a few Months after 
fent by Mr. John Collins to Dr. Barrow at Cambridge, and by 
Dr. Barrow communicated, to Mr. Newton (now Sir Ifaac 
Newton) in June 1669. Whereupon Dr Barrorv mutually fent 
to Mr. Collins a Trad: of Mir. Newtons entituled Analyfis per 
tquationes numero terminorum infinitas . And this is- the frit 
Piece publiflied in the Commercium , and contains a general 
Method of doing in all Figures, what my Lord Brourker and 
Mr, Mercator did in the Hyperbola alone. Mr. Mercator lived 
above ten Years longer without proceeding further than to the 
fingle Quadrature of the Hyperbola. The Progrefs made by 
Mr. Newton fhews that he wanted not Mr Mercator s A Alliance. 
However, for avoiding Difputes, he fuppofes that my Lord 
Brounker invented, and Mr. Mercator demonltrated, the Series 
for the Hyperbola fome Years before they publiflied iti and, 
by confequence, before he found his general Method. 
The aforefaid Treatffe of Analyfis Mr. Newton, in his Let- 
ter to Mr. Oldenburgb, dated Ottob. 14. 1676, mentions in the 
following Manner. Eo ipfo tempore quo Mercatoris Logarithm 
moteebniaprodiit, communicatum eft per ami cum D. Barrow ( tunc 
Mathefeos Prcfcjforem Cantab ) cum D. Collinio Compendium 
quoddam harum Serierum y in quo (ignificaveram Areas & Longi - 
ttfdjms.Qttrvarum omnium } & Solidorum [uperfeies & content a ex 
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